5

Find the determinant of the matrix:-6...

Question

Find the determinant of the matrix:-6

Find the determinant of the matrix: -6



Answers

Find the determinant of the matrix. $$\left[\begin{array}{rr} 6 & 4 \\ -3 & 2 \end{array}\right]$$

However. So here we got this made these two by two matrix and we need to find a the determinant. So we know that there is a very simple formula for two by two matrices to complete the determinant. Okay, so in this case is multiplying the elements on the principle that I don't know so that give us 12 on minus the multiplication off the elements on the other diagonal. Or in this case, that is a two by two matrix on the off diagonal terms. So minus two times minus six, that is equals to 12 on. You can see that in this case the determinants is equal to zero.

So here we got these metrics. Eight. That's the two by two matrix on we can notice. That is on upper triangular matrix. Okay, all the elements below the diagonal are zero. Okay, in this case just went out. But that makes these, uh, matrix and upper triangular matrix on what happened when you got upper triangular matrix or lower triangular matrix matrices. Then the determinant off that matrix is equals to the multiplication off the elements on the diagonal. So that means two times three on that is equal to six. So in this case, the determinant off A equals 26 You can verify this by following the usual procedure. That is, that the determinant off A is equal. The multiplication off the elements on the principle diagonal in this case is six minus the multiplication off the elements on the other diagonal. That means zero. So you can verify that is equals to six

We are given with the determined that is matrix a equals toe negative 5 to 63 hands retirement off a will be close to retirement off the mattress. Negative five toe 63 which will be equal to negative. Five multiplied with three miners, six multiplied with to which is equal to negative 15 miners trail, which is a close to negative 27 that is of attention.

So we're asked to find the determinant of this matrix. So if we think of these entries as a, B, C and D. Since is the two by two matrix, then determinant is A times D minus B times C. Well, eight times d. So that's six times three minus Be it's two times season -5. So that's 18, modest, modest. That's plus two times 5 is 10, so the determine is 28.


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